One-Dimensional Reduction of Multidimensional Persistent Homology
Algebraic Topology
2008-07-28 v2
Abstract
A recent result on size functions is extended to higher homology modules: the persistent homology based on a multidimensional measuring function is reduced to a 1-dimensional one. This leads to a stable distance for multidimensional persistent homology. Some reflections on i-essentiality of homological critical values conclude the paper.
Cite
@article{arxiv.math/0702713,
title = {One-Dimensional Reduction of Multidimensional Persistent Homology},
author = {F. Cagliari and B. Di Fabio and M. Ferri},
journal= {arXiv preprint arXiv:math/0702713},
year = {2008}
}
Comments
16 pages, 11 figures